Extended transition of a nondeterministic finite automaton
= Extended transition of a nondeterministic finite automaton
Without epsilon transitions, define
$$
\widehat\Delta(q,\varepsilon)=\{q\},\qquad
\widehat\Delta(q,wa)=
\bigcup_{p\in\widehat\Delta(q,w)}\Delta(p,a).
$$
A word is accepted when the set reached from the initial state meets the final set.